Haven't touched Octane in a while, but last I tried it couldn't stand up to RedShift in getting rid of noise.
I don't agree. That's like saying we don't need cinematographers to choose lighting set-ups for real sets because there are already some fluorescent fixtures in the ceiling! Just because new tools are making it easier to get realistic lighting results doesn't mean that it doesn't take an artist to tell the computer what to do.

Haha, I guess I got too into the weeds of explaining my technical difficulties to explain the basics of what I did! I also just opened my file and realized I must have messed something up with the orientation of the texture- fixed now in the file attached. I've cleaned it up and made it a little more functional too.
Basically, there is something called the Camera Shader which just takes the view from any camera you link and displays it as a texture. So you can put that texture on an object and it's like a live TV broadcast from the camera to that object. In order for the image to not be stretched, you need that math stuff I posted. One thing that will help visualize it is to turn on Enhanced Open GL and Post Effects:
Now, if you move the null called "Move ME, Scale ME" you should see the texture on the "Mag Display" disc update. Scale it with the scale tool to get greater/less magnification.
Making more sense now?
Magnifier Camera Shader v2.c4d

Yes, much easier to do in AE! But it had me wondering how you would go about it in C4D. I used the Mograph > Camera Shader and a second camera that is way zoomed in. I couldn't figure it out at first why it was always stretching the texture. I assumed that it wanted a square aspect ratio, but when I looked it up in the Help it apparently defaults to 1.33 aspect (what??). I did everything they said, but what wasn't clear to me at first is that the 1.333 actually just represents whatever your project's aspect ratio is currently and you need to figure out the aspect of your object you're projecting on, which for this is just square, so 1. You can replace 1.333 in the equation with, for example, 1.778 for a 16x9 project. Even then, the math just wasn't working out for me. I ended up adding 100 to the multiplied number and putting it in the Vertical Scale field instead of Horizontal like the Help document says. So the final equation is (1/1.778)*100+100 = 156.
Long story short, it can be done!
Magnifier Camera Shader.c4d

Hmmm, maybe have the rotational axis for the cart at the handle. Then use a Target tag to have it aim at a null on the ground plain.... Actually the more I think about it, an IK chain is probably what you want here. Make it like an extention of the hand joint and animate the goal along the ground.

@Vertex Helix for some reason collision wasn't working for me in your file. Is it working for you, @kkamin? If not, I made a new scene that works. One tip is that you at least need enough points on the spline where it will be intersecting. The collision just ignores anything between spline points, so you have to give it enough resolution to work with.
Dog_leash v2.c4d

Right, there is no falling "down" in space, but there is gravity! You might want to consider the Moon's gravity when the two collide. It is less than Earth's, but if you ever watched footage of the Moon Landing, you'd notice they can jump around on there and they don't just fly away :P
Try an Attractor (from the Simulate>Particles menu. Place it at the center of the Moon and see what happens! I set up a simple orbit model really quickly using this method (see file).
Orbit with Attractor.c4d

I assume you're submitting a feature request for creating smoke/fire and other fluid volume effects shipped with C4D? Because there are a couple options for plugins if you need this in Cinema now:
Turbulence FD
X-Particles
If you are making a feature request, I suggest going to MAXON's site for that. There are certainly Cinema developers on this forum, but no guarantee they'll see this.

"Fields" here refers to interlacing, I believe. You do NOT want interlacing, at least not for your render. It can always be added if, heaven forbid, you have to output an interlaced video.
As for your issues with the animation looking "choppy," it's very difficult to evaluate without seeing the animation. Do you get ANY motion blur without activating fields? A shutter speed of 1/50 to me indicates that you haven't activated "Movie Camera," the checkbox at the top of the Physical tab. I haven't used Physcial render in a long time, but I believe this enables motion blur. Then you'll set your Shutter Angle, which defaults to 180. This should give you noticeable motion blur. If I'm wrong, I'd just search YouTube for a tutorial on motion blur with Physical render.

If you never have to see the back of it, you could just model from the front until things don't line up anymore... That's what I'd tell your client is the best possible solution. They're asking for something that is literally mathematically impossible.